If the mother is a good egglayer,
And if the father is of a kind that should be a good egglayer,
Then the babies will probably be good egglayers too.
Similar with egg colors. Red Stars lay brown eggs, so you would usually get some shade of brown from their chicks. Exceptions: if the father is from a white egg breed, you might get white eggs or brown eggs. If the father is from a blue-egg or green-egg breed, you might get green eggs or brown eggs.
What to call them? "Barnyard mix" works well. Red Stars come from a particular cross of two different breeds, so their babies will not be the same as themselves.
(If you do cross Red Star males and females, you'll get some white chicks and some brown ones, browns will be a variety of shades, many will have white markings and some might have black markings. Any color or combination could be male or female.)